Simple word problem involving exponents

[danielle36]

A population of rabbits triples every month. Assume we start out with 100 rabbits.

a. How many rabbits are there after 4 months

b. How long until there are 50,000 rabbits?

Homework Equations

... this is where I am running into the trouble... I'm really not sure how to create the equation to solve these problems...


The only attempt I've made at a solution has been

100 * 3 * 3 * 3 * 3 = amount of rabbits after 4 months?

Any help here would be greatly appreciated

 

[rocomath]

So we know that, at time "0", we have 100 rabbits. Every month the population triples (3x).

$$x(t)=100\times 3^t$$

t=0

$$x(t)=100\times 3^0$$

 

[HallsofIvy]

So your questions become

a. How many rabbits are there after 4 months
What is (100)3⁴?

b. How long until there are 50,000 rabbits?
For what t is (100)3^t= 50000?

For that last one, you will need to use a logarithm. What is log(3^t)?

 

[danielle36]

Ahh.. thank you! I had been staring at that problem for way too long without getting anywhere.. now I'm finally unstuck :)